Experiment to test W=mg

T is thermodynamic temperature and measured in Kelvin degrees of hotness. Root mean square kinetic energy is a determining factor in thermodynamic temperature and mass behaves relativistically under LHC conditions.

For example, you have W = mg - f(T) such that things weigh less at elevated temperature. At the LHC both m and T increase with speed in such a manner that W (the force required to maintain proton beam circulation) increases as beam energies increase, i.e. opposite to your (falsified) notion.